1: Number and Operations

1.1: Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems.

1.1.1: Compare and order real numbers including very large and small integers, and decimals and fractions close to zero.

Adding Fractions (Fraction Tiles)
Comparing and Ordering Decimals
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

1.1.2: Classify real numbers as rational or irrational.

Rational Numbers, Opposites, and Absolute Values

1.1.4: Model and solve problems involving absolute value.

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Rational Numbers, Opposites, and Absolute Values

1.2: Understand and apply numerical operations and their relationship to one another.

1.2.1: Solve problems with factors, multiples, divisibility or remainders, prime numbers, and composite numbers.

Chocomatic (Multiplication, Arrays, and Area)
Finding Factors with Area Models
Operations with Radical Expressions

1.2.2: Describe the effect of multiplying and dividing a rational number by

1.2.2.b: a number between zero and one,

Dividing Fractions
Dividing Mixed Numbers

1.2.2.c: one, and

Dividing Fractions
Dividing Mixed Numbers

1.2.2.d: a number greater than one.

Dividing Fractions
Dividing Mixed Numbers

1.2.3: Solve problems involving percent increase, percent decrease, and simple interest rates.

Compound Interest
Percent of Change

1.2.4: Convert standard notation to scientific notation and vice versa (include positive and negative exponents).

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

1.2.5: Simplify numerical expressions using the order of operations that include grouping symbols, square roots, cube roots, absolute values, and positive exponents.

Order of Operations

2: Data Analysis, Probability, and Discrete Mathematics

2.1: Understand and apply data collection, organization, and representation to analyze and sort data.

2.1.1: Solve problems by selecting, constructing, interpreting, and calculating with displays of data, including box and whisker plots and scatterplots.

Box-and-Whisker Plots
Correlation
Least-Squares Best Fit Lines
Polling: City
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter Plots

2.1.3: Describe how summary statistics relate to the shape of the distribution.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

2.1.4: Determine whether information is represented effectively and appropriately given a graph or a set of data by identifying sources of bias and compare and contrast the effectiveness of different representations of data.

Polling: City
Populations and Samples

2.2: Understand and apply the basic concepts of probability.

2.2.1: Determine theoretical and experimental conditional probabilities in compound probability experiments.

Independent and Dependent Events

2.2.2: Interpret probabilities within a given context and compare the outcome of an experiment to predictions made prior to performing the experiment.

Geometric Probability
Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

2.2.3: Use all possible outcomes (sample space) to determine the probability of dependent and independent events.

Independent and Dependent Events
Theoretical and Experimental Probability

2.3: Understand and demonstrate the systematic listing and counting of possible outcomes.

2.3.2: Solve counting problems and represent counting principles algebraically including factorial notation.

Permutations and Combinations

3: Patterns, Algebra, and Functions

3.1: Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands.

3.1.1: Recognize, describe, create, and analyze numerical and geometric sequences using tables, graphs, words, or symbols; make conjectures about these sequences.

Arithmetic and Geometric Sequences
Finding Patterns
Function Machines 1 (Functions and Tables)
Square Roots

3.2: Describe and model functions and their relationships.

3.2.1: Sketch and interpret a graph that models a given context; describe a context that is modeled by a given graph.

Quadratics in Polynomial Form

3.2.2: Determine if a relationship represented by a graph or table is a function.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Functions
Points, Lines, and Equations
Quadratics in Polynomial Form
Radical Functions

3.2.3: Write the rule for a simple function using algebraic notation.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Points, Lines, and Equations

3.2.4: Identify functions as linear or nonlinear and contrast distinguishing properties of functions using equations, graphs, or tables.

Absolute Value with Linear Functions
Exponential Functions
Function Machines 3 (Functions and Problem Solving)
Graphs of Polynomial Functions
Introduction to Exponential Functions
Linear Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Radical Functions

3.2.5: Demonstrate that proportional relationships are linear using equations, graphs, or tables.

Compound Interest
Direct and Inverse Variation

3.3: Represent and analyze mathematical situations and structures using algebraic representations.

3.3.1: Write or identify algebraic expressions, equations, or inequalities that represent a situation.

Absolute Value Equations and Inequalities
Comparing and Ordering Decimals
Compound Interest
Linear Functions
Simplifying Algebraic Expressions II
Using Algebraic Equations

3.3.3: Analyze situations, simplify, and solve problems involving linear equations and inequalities using the properties of the real number system.

Compound Inequalities
Linear Inequalities in Two Variables
Solving Algebraic Equations II
Solving Two-Step Equations

3.3.4: Translate between different representations of linear equations using symbols, graphs, tables, or written descriptions.

Absolute Value with Linear Functions
Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Solving Equations by Graphing Each Side
Standard Form of a Line

3.3.5: Graph an inequality on a number line.

Absolute Value Equations and Inequalities
Comparing and Ordering Decimals
Compound Inequalities
Rational Numbers, Opposites, and Absolute Values
Solving Linear Inequalities in One Variable

3.4: Analyze how changing the values of one quantity corresponds to change in the values of another quantity.

3.4.1: Interpret the relationship between a linear equation and its graph, identifying and computing slope and intercepts.

Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

4: Geometry and Measurement

4.1: Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships.

4.1.1: Identify the attributes of circles: radius, diameter, chords, tangents, secants, inscribed angles, central angles, intercepted arcs, circumference, and area.

Chords and Arcs
Circles
Circumference and Area of Circles
Inscribed Angles

4.1.2: Predict results of combining, subdividing, and changing shapes of plane figures and solids.

Area of Triangles
Circles
Dilations
Reflections
Rock Art (Transformations)
Rotations, Reflections, and Translations
Translations

4.1.3: Use proportional reasoning to determine congruence and similarity of triangles.

Beam to Moon (Ratios and Proportions)

4.1.4: Use the Pythagorean Theorem to solve problems.

Circles
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard

4.2: Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations.

4.2.1: Model the result of rotations in multiples of 45 degrees of a 2-dimensional figure about the origin.

Rotations, Reflections, and Translations

4.2.3: Identify lines of symmetry in plane figures or classify types of symmetries of 2-dimensional figures.

Holiday Snowflake Designer
Quilting Bee (Symmetry)
Rock Art (Transformations)

4.3: Specify and describe spatial relationships using rectangular and other coordinate systems while integrating content from each of the other strands.

4.3.2: Use the Pythagorean Theorem to find the distance between two points in the coordinate plane.

Circles
Distance Formula

4.4: Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.

4.4.1: Solve problems involving conversions within the same measurement system.

Unit Conversions

4.4.2: Solve geometric problems using ratios and proportions.

Beam to Moon (Ratios and Proportions)
Percents and Proportions
Proportions and Common Multipliers

4.4.3: Calculate the surface area and volume of rectangular prisms, right triangular prisms, and cylinders.

Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders

4.4.6: Describe the relationship between the volume of a figure and the area of its base.

Pyramids and Cones